Quiz — 2009c.pdf

Question 1 sur 5 10:00

[{"id":725,"question":"Quelle est la solution de l'équation 3x - 5 = 2x + 7 ?","option_a":"x = 12","option_b":"x = -12","option_c":"x = 2","option_d":"x = -2","option_e":"","option_f":"","bonne_reponse":"a","explication":"Pour résoudre 3x - 5 = 2x + 7, soustrayez 2x des deux côtés : x - 5 = 7. Puis ajoutez 5 : x = 12. Vérifiez en remplaçant x par 12 dans l'équation initiale.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x = 12\", \"b\": \"x = -12\", \"c\": \"x = 2\", \"d\": \"x = -2\"}}","_debug_options_count":4},{"id":726,"question":"Dans un triangle rectangle, si l'hypoténuse mesure 10 cm et un côté mesure 6 cm, quelle est la longueur du troisième côté ?","option_a":"8 cm","option_b":"√64 cm","option_c":"√136 cm","option_d":"4 cm","option_e":"","option_f":"","bonne_reponse":"b","explication":"D'après le théorème de Pythagore : hypoténuse² = côté1² + côté2². Ici, 10² = 6² + côté2² → 100 = 36 + côté2² → côté2² = 64 → côté2 = √64 = 8 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"8 cm\", \"b\": \"√64 cm\", \"c\": \"√136 cm\", \"d\": \"4 cm\"}}","_debug_options_count":4},{"id":727,"question":"Factorisez l'expression : 4x² - 9.","option_a":"(2x - 3)(2x + 3)","option_b":"(4x - 9)(x + 1)","option_c":"(2x - 3)²","option_d":"(x - 3)(4x + 3)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Il s'agit d'une différence de carrés : a² - b² = (a - b)(a + b). Ici, 4x² - 9 = (2x)² - 3² = (2x - 3)(2x + 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"(2x - 3)(2x + 3)\", \"b\": \"(4x - 9)(x + 1)\", \"c\": \"(2x - 3)²\", \"d\"","_debug_options_count":4},{"id":728,"question":"Un carré a une aire de 49 m². Quel est son périmètre ?","option_a":"28 m","option_b":"14 m","option_c":"7 m","option_d":"56 m","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'aire d'un carré est côté². Si aire = 49 m², alors côté = √49 = 7 m. Le périmètre est 4 × côté = 4 × 7 = 28 m.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"28 m\", \"b\": \"14 m\", \"c\": \"7 m\", \"d\": \"56 m\"}}","_debug_options_count":4},{"id":729,"question":"Quelle est la valeur de x dans l'inéquation : 5x + 3 \u003E 2x + 12 ?","option_a":"x \u003E 3","option_b":"x \u003C 3","option_c":"x \u003E -3","option_d":"x \u003C -3","option_e":"","option_f":"","bonne_reponse":"a","explication":"Soustrayez 2x des deux côtés : 3x + 3 \u003E 12. Puis soustrayez 3 : 3x \u003E 9. Divisez par 3 : x \u003E 3. L'inéquation signifie que x doit être strictement supérieur à 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"x \u003E 3\", \"b\": \"x \u003C 3\", \"c\": \"x \u003E -3\", \"d\": \"x \u003C -3\"}}","_debug_options_count":4}]